基于非线性优化的长宽比未知矩形的位姿测量

提出一种新的基于非线性优化的长宽比未知矩形的位姿测量算法．该算法利用矩形顶点对应的4个像点，可有效地估计出矩形长宽比，并且给出矩形目标跟相机之间的相对姿态以及在矩形边长尺度下的相对位置．在该算法中，为了消除相对位姿和长宽比对计算精度的相互影响，将原问题分解为求解相对位姿和求解长宽比两个子问题．对求解相对姿态子问题建立关于相对位姿的代价函数，采用SE（3）李群的方法对相对位姿进行表示，通过优化代价函数对位姿进行求解；对求解长宽比子问题采用二分法搜索最优值的求解方法．通过实验验证了该算法在使用4个像点进行长宽比估计时的有效性和实时性．其相对计算误差小于3%，而且算法在普通PC上可以满足实时测量位姿的需求．

Position-pose Measurement of Rectangle with Unknown Aspect Ratio Based on Nonlinear Optimization

We propose a novel algorithm, based on nonlinear optimization, for calculating the position pose measurement of a rectangle with an unknown aspect ratio. With only four corresponding corner points of the rectangle, the proposed algorithm can effectively estimate its aspect ratio, the relative pose between the rectangle and the camera, and the relative position, as determined by the unit length of the side of the rectangle. By separating the calculation into two steps: the estimations of the relative position-pose and then the aspect ratio, we establish the cost function of the position pose matrix, which is represented by the theory of the Lie group. By optimizing the cost function, the position pose matrix is solved, and by using a binary search algorithm we obtain the best estimation of the aspect ratio. Our experimental results show that by using four corresponding image points we can estimate the aspect ratio with less than a 3% error rate. The proposed algorithm can also be run in real-time on a regular PC.